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I would have though the fact that the pilot wave theory uses the (multi-particle) Schroedinger equation, while most modern physics is based on field theory, wou
by contravariant 10y ago
I would have though the fact that the pilot wave theory uses the (multi-particle) Schroedinger equation, while most modern physics is based on field theory, would be more important. So far I've seen no formulation of the pilot wave theory in a way that incorporates fields, or provides some other mechanism to account for things like the annihilation of particles.
- dnautics 10y agoIf I'm not mistaken, It's just formalism. Mathematically a continuous wave function is equivalent to a countably infinite vector space. It can be hard to switch between the two (as a chemist we are taught Schroeder and I have a hard time wrapping my head around Heisenberg)
- chestervonwinch 10y ago> a continuous wave function is equivalent to a countably infinite vector space I think you mean that the function is a point in the vector space. More precisely, it is a point in a particular separable Hilbert space, i.e., a complete vector space equipped with an inner product that has countable, dense basis.
- dnautics 10y agoright, sorry. The space of continuous wave functions are equivalent to a countably infinite vector space.
- naasking 10y agoThere are plenty of field theory extensions for Bohmian mechanics. Due the relatively few people working on it, no single approach has become dominant.
- jostylr 10y agoThere are various versions, but the one I recommend to date loses determinism (that was never the point) and allows for annihilation and creation of particles: https://arxiv.org/abs/quant-ph/0208072 https://arxiv.org/abs/quant-ph/0208072 In addition, the ideas of Bohmian mechanics has led to a new direction in dealing with the divergences in QFT, that is, in finding a version of it that is mathematically well-defined: https://arxiv.org/abs/1506.00497 https://arxiv.org/abs/1506.00497